论文标题
在某些dirichlet $ l $ functions的时刻
On the Moments of Certain Families of Dirichlet $L$-functions
论文作者
论文摘要
在本文中，我们解决了计算渐近公式的问题，以预期值和第二次矩值$ l $ l $ functions $ l（1/2，χ_{8D} \otimesψ）$当$ n $ quardirive drimitive drimitive drimive drimive qualulus $ q $ q $ q $，$ q $，$ q $， $ d \ equiv h \ pmod r $是奇数和squarefree，$ r \ equiv0 \ pmod q $偶数。限制对这些算术的进步可确保由Conrey，Farmer，Keating，Rubinstein和snaith.Soundararajan以前限制了这些数量的限制，从而限制了这些数量，从而限制了这些量的进步。我们在本文中进行的非对角线术语需要明显更详细的分析。
In this paper we address the problem of computing asymptotic formulae for the expected values and second moments of central values of primitive Dirichlet $L$-functions $L(1/2,χ_{8d}\otimesψ)$ when $ψ$ is a fixed even primitive non-quadratic character of odd modulus $q$, $χ_{8d}$ is a primitive quadratic character, $d\equiv h\pmod r$ is odd and squarefree and $r\equiv0\pmod q$ is even. Restricting to these arithmetic progressions ensures that the resulting sets of $L$-functions each form a ``family of primitive $L$-functions" in the specific sense defined by Conrey, Farmer, Keating, Rubinstein and Snaith. Soundararajan had previously computed these quantities without restricting them to arithmetic progressions. It turns out that the restriction to arithmetic progressions introduces non-diagonal terms that require significantly more detailed analysis which we carry on in this paper.
